MATHEMATICAL MODELING OF STABLE CARBON ISOTOPE RATIOS IN NATURAL GASES

Abstract

A new approach is presented for mathematical modeling of stable carbon isotope ratios in hydrocarbon gases based on both theoretical and experimental data. The kinetic model uses a set of parallel first-order gas generation reactions in which the relative cracking rates of isotopically substituted (k∗) and unsubstituted (k) bonds are represented by the equation where R is the gas constant and T is temperature. Quantum chemistry calculations have been used to estimate the entropic (Af*/Af) and enthalpic (ΔEa) terms for homolytic bond cleavage in a variety of simple molecules. For loss of a methyl group from a short-chain n-alkane (≤ C6), for example, we obtain an average ΔEa of 42.0 cal/mol and an average Af*/Af of 1.021. Expressed differently, ¹³C-methane generation is predicted to be 2.4% (24‰) slower than ¹²C-methane generation (from a short-chain n-alkane) in a sedimentary basin at 200°C but only 0.7% (7‰) slower in a laboratory heating experiment at 500°C. Similar calculations carried out for homolytic bond cleavage in other molecules show that with few exceptions, ΔEa varies between 0 and 60 cal/mol and Af*/Af between 1.00 and 1.04. Examination of this larger data set reveals: (1) a weak sigmoid relationship between ΔEa and bond dissociation energy; and (2) a strong positive correlation between ΔEa and Af*/Af.